Renormalized entropy solutions of homogeneous Dirichlet problems for quasilinear anisotropic degenerate parabolic-hyperbolic equations

Abstract

We study the well-posedness of renormalized entropy solutions for quasilinear anisotropic degenerate parabolic-hyperbolic equation of the type $\partial_{t}u+\text{div}f(u)=\nabla\cdot(a(u)\nabla u)$ in a bounded domain with general $L^{1}$ initial data and homogeneous Dirichlet boundary condition. We use the device of doubling variables to prove the uniqueness and use the vanishing viscosity method to prove the existence.

Article information

Source
Adv. Differential Equations Volume 19, Number 3/4 (2014), 387-408.

Dates
First available in Project Euclid: 30 January 2014